Evolution of Mixed-State Regions in Type-II Superconductors

Chaocheng Huang; Tom Svobodny

doi:10.1137/S003614109731504X

Evolution of Mixed-State Regions in Type-II Superconductors

Chaocheng Huang, Tom Svobodny

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C ^1+α (Ω ₀ ) for all t > Ω, where Ω ₀ is the initial vortex region that is assumed to be in C ^1+α . Consequently, for any time t , the vortex region Ω _t is of C ^1+α , and the vorticity is in C ^α (Ω _t ).

Original language	American English
Journal	SIAM Journal on Mathematical Analysis
Volume	29
DOIs	https://doi.org/10.1137/S003614109731504X
State	Published - Jul 1 1998

Keywords

high-temperature superconductor
nonequilibrium superconductivity
mixed-state region
vorticity
London equations

Disciplines

Applied Mathematics
Applied Statistics
Mathematics
Physical Sciences and Mathematics
Statistics and Probability

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Evolution of Mixed-State Regions in Type-II SuperconductorsFinal published version, 220 KBLicense: CC BY

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title = "Evolution of Mixed-State Regions in Type-II Superconductors",

abstract = " A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C 1+α (Ω 0 ) for all t > Ω, where Ω 0 is the initial vortex region that is assumed to be in C 1+α . Consequently, for any time t , the vortex region Ω t is of C 1+α , and the vorticity is in C α (Ω t ).",

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AU - Svobodny, Tom

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N2 - A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C 1+α (Ω 0 ) for all t > Ω, where Ω 0 is the initial vortex region that is assumed to be in C 1+α . Consequently, for any time t , the vortex region Ω t is of C 1+α , and the vorticity is in C α (Ω t ).

AB - A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C 1+α (Ω 0 ) for all t > Ω, where Ω 0 is the initial vortex region that is assumed to be in C 1+α . Consequently, for any time t , the vortex region Ω t is of C 1+α , and the vorticity is in C α (Ω t ).

KW - high-temperature superconductor

KW - nonequilibrium superconductivity

KW - mixed-state region

KW - vorticity

KW - London equations

UR - https://corescholar.libraries.wright.edu/math/45

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VL - 29

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

ER -

Evolution of Mixed-State Regions in Type-II Superconductors

Abstract

Keywords

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